Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation

Ermentrout, G. Bard; Kopell, Nancy

doi:10.1137/0146017

Cited by 555 publications

(523 citation statements)

References 34 publications

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“…It is formally equivalent to the Theta neuron (Ermentrout and Kopell 1986) and has been often used in computational studies because it has analytical solutions for many input signals. In our study, we use the version used by , given by…”

Section: Quadratic Integrate and Firementioning

confidence: 99%

Gamma oscillations as a mechanism for selective information transmission

2010

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In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin-Huxley (HH) neuron] and that of excitatory-inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.

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Section: Quadratic Integrate and Firementioning

confidence: 99%

Gamma oscillations as a mechanism for selective information transmission

2010

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“…For each neuron, we use a one-dimensional theta model in a manner similar to that described in Börgers and Kopell (2003). This canonical model can be attained by a change of variables from a quadratic integrate-and-fire model (Börgers et al 2005) or from a Hodgkin-Huxley type I neuron (Ermentrout and Kopell 1986). In this model, the cell is represented by a point traveling along a circle.…”

Section: Simplified Modelmentioning

confidence: 99%

Modeling Gaba Alterations in Schizophrenia: A Link Between Impaired Inhibition and Altered Gamma and Beta Range Auditory Entrainment

Vierling-Claassen¹,

Siekmeier²,

Stufflebeam³

2008

Schizophrenia Research

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Vierling-Claassen D, Siekmeier P, Stufflebeam S, Kopell N. Modeling GABA alterations in schizophrenia: a link between impaired inhibition and altered gamma and beta range auditory entrainment. J Neurophysiol 99: 2656 -2671, 2008. First published February 20, 2008 doi:10.1152/jn.00870.2007. The disorganized symptoms of schizophrenia, including severely disordered thought patterns, may be indicative of a problem with the construction and maintenance of cell assemblies during sensory processing and attention. The gamma and beta frequency bands (15-70 Hz) are believed relevant to such processing. This paper addresses the results of an experimental examination of the cortical response of 12 schizophrenia patients and 12 control subjects when presented with auditory click-train stimuli in the gamma/beta frequency band during measurement using magnetoencephalography (MEG), as well as earlier work by Kwon et al. These data indicate that control subjects show an increased 40-Hz response to both 20-and 40-Hz stimulation as compared with patients, whereas schizophrenic subjects show a preference for 20-Hz response to the same driving frequencies. In this work, two computational models of the auditory cortex are constructed based on postmortem studies that indicate cortical interneurons in schizophrenic subjects have decreased GAT-1 (a GABA transporter) and GAD 67 (1 of 2 enzymes responsible for GABA synthesis). The models transition from control to schizophrenic frequency response when an extended inhibitory decay time is introduced; this change captures a possible effect of these GABA alterations. Modeling gamma/beta range auditory entrainment in schizophrenia provides insight into how biophysical mechanisms can impact cognitive function. In addition, the study of dynamics that underlie auditory entrainment in schizophrenia may contribute to the understanding of how gamma and beta rhythms impact cognition in general.

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“…Thus, if one understands these simple models, it is possible to apply that knowledge to whole classes of model cells. For example, the action-potential generation of many conductance-based models, which are Class I can be well-fit with the quadratic integrate-and-fire model [9]:…”

Section: Neural Oscillationsmentioning

confidence: 99%